45619 ÷ 6 = 7603 R1
Alright, let's work through the division of 45619 by 6 step by step.

Step 1:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 6

Step 2:
6 goes into 45 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 42 from 45 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 3:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 76
Subtract 36 from 36 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 4:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 760
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 5:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 7603
Subtract 18 from 19 to get 1.

The final result is 7603 with a remainder of 1.